According to the continuity equation in fluid dynamics, which states that mass flow rate is constant within a system, the product of the cross-sectional area and velocity remains constant along the flow direction.
In this scenario, if the flow rate is constant at 2.5 mgd (million gallons per day), the cross-sectional area of the pipe does not change. Therefore, any changes in velocity must correspond to changes in pressure or energy.
When the pressure energy of the flowing water is converted to velocity head, as described by Bernoulli's principle, the velocity increases while the pressure decreases. This is due to the conservation of energy in the system.
In the given situation, the pressure energy of 35 psi is converted to velocity head. As a result, the pressure decreases and the velocity increases. The exact relationship between pressure and velocity changes can be determined using the Bernoulli equation, which relates pressure, velocity, and elevation in a flowing fluid system.
In summary, if the flow rate remains constant according to the continuity equation, the increase in velocity occurs because the pressure energy is converted into velocity head, resulting in a decrease in pressure and an increase in velocity.